What the text says. "But when Gallio was proconsul of Achaia, the Jews with one accord rose up against Paul and brought him before the judgment-seat" (Acts 18:12, ASV). Gallio throws the case out.
What was found. In 1905 a French excavation team working at the Temple of Apollo at Delphi recovered fragments of a Greek inscription, nine fragments in all, further pieces coming to light over following years, carrying a letter of the emperor Claudius to Delphi. The emperor writes of his long goodwill toward the city and his care for the cult of Pythian Apollo, and, hearing that Delphi is short of citizens, directs that new inhabitants be invited. The relevant clause is the source of his information: he has it, he says, from "my friend and proconsul L. Iunius Gallio", Lucius Junius Gallio, the Gallio of Acts. The letter carries Claudius' own titles, and those are a date: he is named as holding the tribunician power for the 12th time and acclaimed Imperator for the 26th time, a combination scholars place in the first half of AD 52.
Why it matters, and what it does not do. A proconsul of a senatorial province such as Achaia normally took office around midsummer and served a single year. An imperial letter of early-to-mid AD 52 that names Gallio as proconsul therefore places his term across AD 51-52, and Luke says Paul was in Corinth, for eighteen months, when Gallio held that office. That converts a New Testament episode into a dated one, and because Paul's other movements are tied to the Corinthian stay by Acts and the letters, the whole Pauline chronology can be pinned to it. It is commonly called the anchor point of New Testament dating, and it is the strongest such anchor we have.
Two honest limits. The stone dates Claudius' letter, not Paul's hearing: it fixes Gallio's proconsulship to within about a year, and Paul's trial to somewhere inside it, not to a month. And scholars still differ over the exact reckoning, whether Gallio's year ran 51-52 or 52-53 turns on how the acclamation is counted and on when precisely he took up and left the post, which Seneca says he did early, on account of a fever.
The anchor is firm to about a year; it is not firm to a date.
Sources: Acts 18:12-17; the Delphi inscription (É. Bourguet, first published 1905); ISBE 1915, "Gallio"; Seneca, Epistulae Morales 104.1.
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